**** Read.me file for MultiSum.m **** **** written by Kurt Wegschaider, April 1997 **** **** Research Institute for Symbolic Computation **** **** Johannes Kepler Universitaet, A- 4040 Linz, Austria **** **** http://www.risc.uni-linz.ac.at/research/combinat/risc/ **** **** email: Kurt.Wegschaider@risc.uni-linz.ac.at **** The Mathematica package MultiSum contains functions to prove binomial multisum identities. It is based on a generalization of Sister Celine's technique and proves identities by finding a recurrence for the summand from which we can gain a recurrence for the sum. The package and the underlying method are described in the following diploma thesis: Kurt Wegschaider, "Computer Generated Proofs of Binomial Multi-Sum Identities", RISC Linz, J. Kepler Universitaet Linz, Austria, 1997. http://www.risc.uni-linz.ac.at/research/combinat/software/MultiSum/pub/wegschaider97.ps http://www.risc.uni-linz.ac.at/publications/download/risc_2245/diplom.ps In this file we only give a short introduction in how to use the package. Details can be found in the above mentioned diploma thesis. The package is loaded by In[1]:= < MyOwnNullSpace, Protocol -> True] where MyOwnNullSpace is the name of any Mathematica function with the same input-output behaviour as the builtin "NullSpace". (The Mathematica builtin function is unusably slow, so we use "ENullSpace", written by E. Aichinger). The current value of the options can be seen with In[7]:= Options[ MultiSum] As a special feature, the RISC users of the package can use an efficient nullspace function "CNullSpace", written by E. Aichinger, that works outside of Mathematica and uses the SACLIB (see E. Aichinger, "A linear system solver for Mathematica that uses SACLIB (Version 1.0)", RISC Technical Report 97-05.) It can be used as follows In[8]:= < CNullSpace] For more details on the MultiSum package see the above mentioned diploma thesis.